Sunday 6 & Tuesday 8 December are both religious holidays in Fuerteventura.
I don't know about the other supermarkets, but Mercadona will be closed on Tuesday.
So they have a nice long break, some businesses will also be closed on Monday.
No doubt there will be another hiatus with postal deliveries!
As it's a Sunday, the official public holiday will be the Monday so yes, government offices and some businesses will be closed. But it won't have a great effect on most supermarkets and shops in tourist resorts and none on bars and restaurants.
PS Actually, I think the 6th is Constitution Day - nothing religious about that, but it has the same effect of course.